About the finite groups whose minimal normal subgroups are union of two conjugacy classes exactly

Summary

In this paper we classify all the finite groups G satisfying β(G)=r(G) — α(G) - 1 where r(G) is the number of conjugacy classes of G, β(G) the number of minimal normal subgroups of G, S(G) the socle of G and α(G) the number of conjugacy classes of G out of S(G), and such that ¦G/S(G)¦ is divisible for at most three prime numbers.